To produce g, function f was reflected over the x-axis andFunction g can be defined as

∠1 and ∠2 have equal measures because they are corresponding angles

Hello there. To solve this question, we'll have to remember which other formulas for area of triangles can be used.

Most specifically, it asks for a formula that works on an obtuse triangle, that is, a triangle that haves an angle that measures more than 90º.

Besides the formula BH/2, that refers to half of the product between the measurements of the base and the height of the triangle, of course, this height must be a projection perpendicular to the base, as in the following drawing:

Another formula that can be used is Heron's formula;

Knowing the measures of all the sides of the triangle (no matter if it is an obtuse, acute or right triangle), say a, b and c, Heron's formula states that the area S of the triangle is given by:

Where

is the semiperimeter of the triangle.

This is the answer we've been looking for.

Answer:

x = 3/2 = 1.5

Explanation:

The initial equation is:

To solve the equation, we need to multiply both sides by 250 as:

This fraction can be simplified as:

Therefore, the value of x is 3/2 as a fraction or it is 1.5 as a decimal.

y represents the distance of the snail to the flower, in ft

x represents time, in hours

In the beginning, the distance of the snail to the flower is 7 feet. Then, the point (0, 7) is on the graph

After the first hour, the snail crawls 2 feet, then its distance to the flower is 7 - 2 = 5 ft. Then, the point (1, 5) is on the graph.

After the second hour, the snail crawls another 2 feet, then its distance to the flower is 5 - 2 = 3 ft. Then, the point (2, 3) is on the graph.

After the third hour, the snail crawls another 2 feet, then its distance to the flower is 3 - 2 = 1 ft. Then, the point (3, 1) is on the graph.

The graph is

There are a total of 4 outcomes that involve choosing a blue marble

Here, we want to write a sample space for the selection

For us to have the sample space, we will have to write out the possible outcomes

We shall be representing the blue marble by b, the green by g and the yellow by y

We have the sample space as follows;

{1B,1G,1Y,2B,2G,2Y,3B,3G,3Y,4B,4G,4Y}

From the sample space, we can see that there are actually 12 possible results

Now, to get the outcomes involving blue marbles, we simply select the members of the sample space having B at the back

We have these as 1B, 2B, 3B and 4B

This is a total of 4 outcomes

Answer:

35 degrees.

Explanation:

The figure shown is an isosceles triangle. An isosceles triangle has two of its sides and base angles to be equal.

Since the sum of the angles in a triangle is 180 degrees, hence:

110 + (base angles) = 180

110 + (<1 + <1) = 180 (since base angles are the same)

110 + 2<1 = 180

2<1 = 180-110

2<1 = 70

Divide both sides by 2

2<1/2 = 70/2

<1 = 35 degrees

Hence the angle between an eave and the horizontal support beam is 35 degrees.

Given: The odds in favor of receiving a gift are 4/19.

Required: To determine the probability of receiving a gift.

Explanation: The probability of an event A that has an odd of happening as A/B can be calculated as

Here A=4 and B=19. Putting the values, we get,

Final Answer: The probability of Brian receiving a gift is 4/23.

The sequence is arithmetic because the common difference is 4.

Answer:

the sequence is arithmetic. the cd is 4

Step-by-step explanation:

1 + 4 = 5

5 + 4 = 9

9 + 4 = 13

Subtract the second equation from the first,

Given that 150 is increased to 861

The absolute change formula is

Where

The new value = 861

The old value = 150

The absolute change is

Hence, the absolute change is 711

The formula for percentage is

Substitute the values into the percentage change formula

Hence, the percentage change is 474% increase

12h 2 minutes and 5 seconds

1) Adding 3 hours 6 minutes and 45 seconds to 8 hours 55 minutes and 20 seconds we can write like this:

2) Every time we hit 60'' (seconds) we add to its neighbor then we can find the following sum.

1h ----60'

1 minute ----60''

3) Then the sum of those is equal to 12h 2 minutes and 5 seconds

Hello there. To solve this question, we'll have to remember some properties about set up an equation and solving them.

"Let y be an unknown number. 18 times a number minus 97 is equal to 9 less than the number."

We need to find this number.

Starting with the equation:

On the left hand side, we have 18y as 18 times the number, then subtracted 97 for the minus 97 part. On the right hand side, 9 less than the number is represented as the number minus 9.

So, subtract y - 97 on both sides of the equation

Divide both sides of the equation by a factor of 17

This is the number we've been looking for.

Answer:

80

Step-by-step explanation:

This is a ratio and we can set it up as follows and solve for x:

[tex]\frac{2}{3} = \frac{x}{120}[/tex]

Multiply both sides by 120

80 = x

An ordered pair for the equation 5x + y = 1 is (0, 1)

The equation of the function is given as

5x + y = 1

To determine the ordered pair, we simply set the value of x to any value.

And then calculate the value of y

Using the above parameters as a guide, we can assume that

x = 0

Substitute x = 0 in 5x + y = 1

5(0) + y = 1

Evaluate the product

0 + y = 1

So, we have

y = 1

Express as ordered pairs

(x, y) = (0, 1)

Hence, the ordered pair in the solution is (0, 1)

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An ordered pair of the equation 5x + y = 1 is (1, - 4).

An ordered pair (a,b) is a set of values for x and y coordinates.

As the name suggests (a, b) and (b, a) are two different ordered pairs.

Given, 5x + y = 1.

Or,

y = 1 - 5x.

Now we can choose any arbitrary value of x that corresponds to a value

of y.

At x = 1,

y = 1 - 5(1).

y = 1 - 5,

y = - 4.

∴ An ordered pair o the given equation 5x + y = 1 is (1, - 4).

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The question provides the following information;

Money at hand = 73.50

Money earned = x

Purchases made = 99.99

Money left over = 23.51

These sets of numbers can be put into an equation as shown below;

(73.5 + x) - 99.99 = 23.51

This equation means what you had at the beginning plus what earned from mowing lawns is a total of 73.5 + x. Subtract the cost of shoes purchased from this total and you'll now have a balance of 23.51

We can now solve for the money earned from mowing lawns as follows;

(73.5 + x) - 99.99 = 23.51

Add 99.99 to both sides of the equation (in order to isolate the 73.5 + x on the left side of the equation). You now have;

73.5 + x = 123.5

Next you subtract 73.5 from both sides of the equation (in order to isolate the x on the left hand side)

x = 50

This means the money earned from mowing lawns is $50

The ratio of width to height is :

If h = 18 inches, the value of w will be :

The answer is w = 29.12 inches

The five credit score tiers are listed in ascending order, starting with the lowest tier:

Deep Subprime < Subprime < near prime < prime < superprime

The ability of a consumer to get credit may be significantly influenced by their credit score. These interactive graphs demonstrate how lending behavior has changed for different credit score profiles of borrowers.

We concentrate on the following five commercially available credit score levels:

Subprime's credit scores is between 580 to 619.

Prime's credit score level is between 660 to 719.

The credit score level of deep subprime is below 580.

The credit score level of near prime is 620 - 659.

The credit score level of superprime is 720 or above.

Therefore, the five tires of credit scores from lowest to highest are:

Deep Subprime < Subprime < near prime < prime < superprime

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Answer:

Angle Reason

m∠ECD = 140 Given

m∠ECB = 40 Supplementary angles

m∠EBC = 70 Isosceles triangle

m∠ABE = 110 Supplementary angles

Explanation:

Angle ECB and CED are supplementary because they form a straight line and their sum is 180 degrees. So, we can calculate the measure of ∠ECB as

m∠ECB = 180 - 140

m∠ECB = 40

Then, the interior sum of the angles of a triangle is equal to 180 degrees, so

m∠ECB + m∠EBC + m∠BEC = 180

40 + m∠EBC + m∠BEC = 180

However, m∠EBC = m∠BEC because triangle ABC is an isosceles triangle where 2 sides have the same length BC and EC. So, we can find m∠EBC as follows

40 + m∠EBC + m∠EBC = 180

40 + 2m∠EBC = 180

40 + 2m∠EBC - 40 = 180 - 40

2m∠EBC = 140

m∠EBC = 140/2

m∠EBC = 70

Then, the measure of ∠ABE is equal to

∠ABE = 180 - m∠EBC

∠ABE = 180 - 70

∠ABE = 110

Therefore, we can answer it as follows

Angle Reason

m∠ECD = 140 Given

m∠ECB = 40 Supplementary angles

m∠EBC = 70 Isosceles triangle

m∠ABE = 110 Supplementary angles

To obtain the slope of the line that passes through the two given points, the following steps are recommended:

Step 1: Recall the formula for the slope of a line that passes through any two points (x1, y1) and (x2, y2), as follows:

Step 2: Apply the formula to find the slope of the line that passes through the points (4, -9) and (8, -3), as follows:

Therefore, the slope of the line that passes through the points (4, -9) and (8, -3) is 3/2

The most appropriate choice for congruency of triangles will be given by

[tex]\bar{IL} \cong \bar{JP}[/tex]

Third option is correct.

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are equal.

There are five axioms of congruency. They are

SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom.

Here,

ΔIKL ≅ ΔJOP [Given]

[tex]\bar{IL} \cong \bar{JP}[/tex] [Corrosponding parts of congruent triangles are congruent]

Third option is correct.

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Complete Question

The diagram with the question has been attached below

We determine the greatest common factor as follows:

So, we factor:

So, the greatest common factor is 2n^3.

Sum of the exterior angles of a polygon = 360°

For a regular polygon, all the angles are equal:

mn = 360

where n = the number of sides

m = the size of an exterior angle

For m = 15°

15n = 360

n = 360/15

n = 24

Therefore, the polygon

Answer:

2 and 3

Explanation:

Given the equation:

Now, observe the following:

Taking the indices:

We'll use the follwowing property, which comes from the definition of a logarithm:

i.e, The logarithm with base a of b is c if, and only if a to the c power equals b.

Using this to translate

Into exponential form, will yield:

Because:

ANSWER:

Remember that a function is a relation between two sets of numbers where the first set is called domain, and the second set is called range.

The main characteristic that defines a function is that a domain element can be associated with only one element of the range set. In other words, one input value cannot have two different output values.

Therefore, the right answer is the third choice

Because this represents a function and its inverse also represents a function, that is, it's inverse have the characteristic of a function. The following set represents the inverse

As you can observe, this inverse set also follows the function definition, because every single input is associated with only one output.

if there was no ratio they were in the middle (4,6)

but in this case we must multiply by the ratio

so

so the C point is

1. At age 65 when you retire, you have (future value) $202,531.69 from the IRA.

2. The total interest earned on the monthly investment of $95 at 6.25% for 40 years is $156,931.69.

The future value, which represents the compounded value of the monthly investments, can be computed using the FV formula or an online finance calculator as follows:

Number of years = 40 (65 - 25)

N (# of periods) = 480 months (40 x 12)

I/Y (Interest per year) = 6.25%

PV (Present Value) = $0

PMT (Periodic Payment) = $95

Results:

Future Value (FV) = $202,531.69

Sum of all periodic payments = $45,600 ($95 x 480 months)

Total Interest = $156,931.69

Thus, the future value of the monthly investment is $202,531.69 with an interest of $156,931.69.

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Let us begin by illustrating the problem using a diagram:

Here we have represented the angle that the driveway makes with the horizontal to be x

Step 1: Label the sides as shown:

Step 2: Using the sides given, find the required angle

The formula that relates the angle, opposite side and hypothenuse side is:

Applying the formula:

Hence, it makes an angle of 7.3 degrees with the horizontal

For this problem, we need to describe a real-life situation where trigonometric functions can be used to model the problem.

Let's assume that a certain vehicle's position is controlled by the speeds of the wheels on each side of the car. Whenever the speeds on the left wheels and right wheels are equal, then the car moves forward, if the speed on the left side is greater than the one on the right side the car goes right, and if the speed on the right side is greater, then the vehicle goes to the left side. This type of car is called a differential drive car, and it's very common on remote-controlled (RC) vehicles.

If we want to model the speed of the car in a two dimensional grid, such as below:

We need to assume that the vehicle will have two components of velocity, one that is parallel to the x-axis and one that is parallel to the y-axis. These will form the linear velocity for the vehicle. We also need an angular velocity, which is the rate at which the angle of the vehicle changes.

If we assume that the wheels of the vehicles are at a distance of "L" apart from each other, then we can model the angular velocity of the vehicle as:

Where "vr" is the speed on the right wheel, and "vl" is the speed on the left wheel. The movement will happen with the center of the car as the center of the movement, with this we can assume that the velocity of the vehicle on the two axes should be:

Therefore we can describe the vehicle speed with the following equations:

The input variables are "vr" and "vl" which are the speeds of each wheel and the angle of the vehicle "theta", the output is the speed at the x coordinate and the speed at the y coordinate, and the angular speed.

This works very well because if the vehicle is moving parallel to the x-axis, the angle will be 0, the cosine of 0 is 1, therefore the speed on the y axis will be 0 and the speed on the x-axis will be given by 0.5(vr+vl). The opposite happens when the vehicle is moving parallel to the y-axis.